Two adjacent angles are on a straight line. One angle has a measure of (5x−28)° and the other angle has a measure of (8x)° . What is the measure of the second angle?(1 point) Responses 120° 120 degrees 128° 128 degrees 16° 16 degrees 52°
Since the two angles are adjacent and on a straight line, their sum should be equal to 180 degrees.
So we have the equation (5x - 28) + (8x) = 180.
Combining like terms, we get 13x - 28 = 180.
Adding 28 to both sides, we have 13x = 208.
Finally, dividing both sides by 13, we get x = 16.
Substituting this value back into the second angle's measure, we get 8x = 8(16) = 128.
Therefore, the measure of the second angle is 128 degrees.
A 180° angle (straight line) is formed by two adjacent angles. One angle has a measure of (2x+3)° and the other has a measure of (x−6)° . What are the measures of the two angles that make up the straight line?(1 point) Responses 129° and 51° 129 degrees and 51 degrees 186° and 88° 186 degrees and 88 degrees 121° and 59° 121 degrees and 59 degrees 125° and 55°
Since the two angles are adjacent and form a straight line, their sum should be equal to 180 degrees.
So we have the equation (2x + 3) + (x - 6) = 180.
Combining like terms, we get 3x - 3 = 180.
Adding 3 to both sides, we have 3x = 183.
Finally, dividing both sides by 3, we get x = 61.
Substituting this value back into the first angle's measure, we get 2x + 3 = 2(61) + 3 = 122 + 3 = 125.
And substituting the value into the second angle's measure, we get x - 6 = 61 - 6 = 55.
Therefore, the measures of the two angles that make up the straight line are 125 degrees and 55 degrees.
Two adjacent angles form a resulting angle with measure 160° . m∠1=3x° and m∠2=(2x+10)° . Solve for x . What are the two unknown angles’ measurements?
Since the two angles are adjacent and form a resulting angle with measure 160°, the sum of the two unknown angles should be equal to 160 degrees.
So we have the equation 3x + (2x + 10) = 160.
Combining like terms, we get 5x + 10 = 160.
Subtracting 10 from both sides, we have 5x = 150.
Finally, dividing both sides by 5, we get x = 30.
Substituting this value back into the first angle's measure, we get 3x = 3(30) = 90.
And substituting the value into the second angle's measure, we get 2x + 10 = 2(30) + 10 = 60 + 10 = 70.
Therefore, the two unknown angles' measurements are 90 degrees and 70 degrees.